TigerVNC configuration on Fedora Linux

On Windows, I can configure the VNC server module, so that when a user is logged in on Windows, I can connect and see the same screen that user sees. On Linux, it appears that the serverr always creates a new virtual screen, and only one instance can be running for each user. I.e., if I am logged in on the console, I cannot log in remotely as the same user. How can I get around this and get to the console frame buffer remotely?